连续力学中的数学模型

出版时间：2003-9  出版社：北京世图  作者：R.Temam,A.Miranville  页数：288  
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内容概要

At a time when mathematical modeling is pervading many areas of science and master's degree programs in industrial mathematics are being initiated in many universities, this book is intended as an introduction to continuum mechanics and mathematical modeling. One of the aims of the book is to reduce the gap slightly between mathematics and this area of natural science - a gap that is usually due to the language barrier and to the differences in thinking and reasoning. This book is written in a style suitable for mathematicians and adapted to their training. We have tried to remain very close to physics and to mathematics at the same time by making, in particular, a clear separation between what is assumed and what is proved. As it is, the book may appeal as well to a broader audience, such as engineers who would like to have a different perspective on the field, relying less on physical intuition, and advanced researchers who would like an introduction to a field new to them.

书籍目录

IntroductionA Few Words About NotationsPART ONE. FUNDAMENTAL CONCEPTS IN CONTINUUM MECHANICS　1 Describing the Motion of a System: Geometry and Kinematics　 1.1 Deformations　　1.2 Motion and Its Observation Kinematics　　1.3 Description of the Motion of a System: Eulerian and Lagrangian Derivatives　　1.4 Velocity Field of a Rigid Body: Helicoidal Vector Fields　　1.5 Differentiation of a Volume Integral Depending on a Parameter　2 The Fundamental Law of Dynamics　　2.1 The Concept of Mass　　2.2 Forces　　2.3 The Fundamental Law of Dynamics and Its First Consequences　　2.4 Application to Systems of Material Points and to Rigid Bodies　　2.5 Galilean Frames: The Fundamental Law of Dynamics Expressed in a Non-Galilean Frame　3 The Cauchy Stress Tensor - Applications　  3.1 Hypotheses on the Cohesion Forces　　3.2 The Cauchy Stress Tensor　　3.3 General Equations of Motion　　3.4 Symmetry of the Stress Tensor　4 Real and Virtual Powers　　4.1 Study of a System of Material Points　　4.2 General Material Systems: Rigidifying Velocities　　4.3 Virtual Power of the Cohesion Forces: The General Case　　4.4 Real Power: The Kinetic Energy Theorem　5 Deformation Tensor, Deformation Rate Tensor,Constitutive Laws　　5.1 Further Properties of Deformations　　5.2 The Deformation Rate Tensor　　5.3 Introduction to Rheology: The Constitutive Laws　6 Energy Equations and Shock Equations　　6.1 Heat and Energy　　6.2 Shocks and the Rankine-Hugoniot RelationsPART TWO. PHYSICS OF FLUIDS　7 General Properties of Newtonian Fluids　　7.1 General Equations of Fluid Mechanics　　7.2 Statics of Fluids　　7.3 Remark on the Energy of a Fluid　8 Flows of Inviscid Fluids　　8.1 GeneralTheorems　　8.2 Plane Irrotational Flows　　8.3 Transsonic Flows　　8.4 Linear Acoustics　9 Viscous Fluids and Thermohydraulics　　9.1 Equations of Viscous Incompressible Fluids　　9.2 Simple Flows of Viscous Incompressible Fluids　　9.3 Thermohydraulics　　9.4 Equations in Nondimensional Form: Similarities　　9.5 Notions of Stability and Turbulence　　9.6 Notion of Boundary Layer　10 Magnetohydrodynamics and Inertial Confinement of Plasmas　　10.1 The Maxwell Equations and Electromagnetism　　10.2 Magnetohydrodynamics　　10.3 The Tokamak Machine　11 Combustion　　11.1 Equations for Mixtures of Fluids　　11.2 Equations of Chemical Kinetics　　11.3 The Equations of Combustion　　11.4 Stefan-Maxwell Equations　　11.5 A Simplified Problem: The Two-Species Model　12 Equations of the Atmosphere and of the Ocean　　12.1 Preliminaries　　12.2 Primitive Equations of the Atmosphere　　12.3 Primitive Equations of the Ocean　　12.4 Chemistry of the Atmosphere and the Ocean　　Appendix: The Differential Operators in Spherical CoordinatesPART THREE. SOLID MECHANICS　13 The General Equations of Linear Elasticity　　13.1 Back to the Stress-Strain Law of Linear Elasticity:　　The Elasticity Coefficients of a Material　　13.2 Boundary Value Problems in Linear Elasticity:The Linearization Principle　　13.3 Other Equations　　13.4 The Limit of Elasticity Criteria　14 Classical Problems of Elastostatics　　14.1 Longitudinal Traction-Compression of a Cylindrical Bar　　14.2 Uniform Compression of an Arbitrary Body……15 Energy Theorems - Duality: Variational Formulations16 Introduction to Nonlinear Constitutive Laws and to Homogenization17 Linear Wave Equations in Mechanics18 The Soliton Equation: The Korteweg-de Vries Equation19 The Nonlinear Schrodinger EquationAppendix The Partial Differential Equations of MechanicsReferencesIndex